Towards Accurate State Estimation: Kalman Filter Incorporating Motion Dynamics for 3D Multi-Object Tracking

TL;DR

The paper addresses the precision gap in 3D MOT state estimation arising from constant-motion Kalman filters. It introduces a novel KF formulation that adaptively incorporates motion dynamics (notably jerk) through weighted state prediction, post-measurement noise mitigation, Gaussian smoothing over a transition window, and normalized dynamic weights, enabling robust localization and trajectory prediction during occlusions. Empirical results on KITTI and Waymo Open Dataset benchmarks show consistent improvements in MOTA and HOTA across detectors, with stronger gains for distant and occluded targets, and a modest runtime overhead of approximately $0.078$ ms per frame, supporting real-time applicability. The work also provides an occlusion-simulation methodology to stress-test MOT under long occlusions, demonstrating substantial gains in long-occlusion scenarios and improved object re-identification.

Abstract

This work addresses the critical lack of precision in state estimation in the Kalman filter for 3D multi-object tracking (MOT) and the ongoing challenge of selecting the appropriate motion model. Existing literature commonly relies on constant motion models for estimating the states of objects, neglecting the complex motion dynamics unique to each object. Consequently, trajectory division and imprecise object localization arise, especially under occlusion conditions. The core of these challenges lies in the limitations of the current Kalman filter formulation, which fails to account for the variability of motion dynamics as objects navigate their environments. This work introduces a novel formulation of the Kalman filter that incorporates motion dynamics, allowing the motion model to adaptively adjust according to changes in the object's movement. The proposed Kalman filter substantially improves state estimation, localization, and trajectory prediction compared to the traditional Kalman filter. This is reflected in tracking performance that surpasses recent benchmarks on the KITTI and Waymo Open Datasets, with margins of 0.56\% and 0.81\% in higher order tracking accuracy (HOTA) and multi-object tracking accuracy (MOTA), respectively. Furthermore, the proposed Kalman filter consistently outperforms the baseline across various detectors. Additionally, it shows an enhanced capability in managing long occlusions compared to the baseline Kalman filter, achieving margins of 1.22\% in higher order tracking accuracy (HOTA) and 1.55\% in multi-object tracking accuracy (MOTA) on the KITTI dataset. The formulation's efficiency is evident, with an additional processing time of only approximately 0.078 ms per frame, ensuring its applicability in real-time applications.

Figures (9)

• Figure 1: State estimation (yellow bounding box) of an off-scene car drifts away from the actual car location (disconnected lines) with the traditional Kalman filter. Meanwhile, the proposed Kalman filter with motion dynamics shows robust localization for the car.
• Figure 2: The graph demonstrates the performance fluctuation in state estimation for three motion models: constant velocity (Red), constant acceleration (Blue), and constant jerk (Green). The top graph compares the Euclidean distance error in state estimation obtained by the three models of the $0005$ stream in the KITTI Geiger2012CVPR dataset. The second row shows graphs of the car's motion dynamics, change in velocity (Blue), and change in acceleration (Red).
• Figure 3: The diagram shows an overview of the proposed Kalman filter incorporating motion dynamics. The flow begins with the prior knowledge of an object's states at time $t-1$. The information includes state uncertainty $P_{t-1|t-1}$, weighted motion dynamics of the object $\hat{W}_{t-1}$, and object's state $\hat{x}_{t-1|t-1}$. This information is used to predict the next state estimation of the object, considering its captured motion dynamics, and adjust the estimated state accordingly. This results in the next state estimation $\hat{x}_{t|t-1}$ and an updated uncertainty $P_{t|t-1}$. With a new measurement, the object's spatial state will be updated to obtain $\hat{x}_{t|t}$, and new motion dynamics will be captured through the Gaussian distribution of changes observed in motion dynamics parameters (Position, velocity, and acceleration). The obtained updated motion dynamics $d_t$ from the Gaussian distribution is weighted to form an updated weighted motion dynamics $\hat{W}_t$. The flow will be repeated in the next time step $t+1$.
• Figure 4: The graph shows the Euclidean distance error comparison between the localization measurements obtained from the employed detector (Blue-line), the updated state estimation of the object's location (Orange-line), and the measurement from the detector with cleared noise by the proposed term $D_t$ (Green-line). The experiment is conducted in two cars over more than $300$ consecutive frames. The numerical values in the legend present the mean square error and standard deviation, respectively.
• Figure 5: The graphs show a car's motion dynamics, which accelerates and decelerates for a particular time stamp. The first graph shows the Euclidean distance error of state estimation from three different motion models: constant velocity (Red), constant acceleration (Blue), and constant Jerk (Green). The second graph shows the corresponding change in traveling distances from the ground truth, presenting the car motion dynamics for velocity. Meanwhile, the third graph shows the car's velocity change compared to the ground truth, illustrating the motion dynamics for acceleration. The last graph shows the change in car acceleration from the ground truth, illustrating the motion dynamics for jerk. The graph highlights three transition states in the motion dynamics of the car: Acceleration (Red dot-line), transition from acceleration to deceleration (Orange dot-line), and deceleration (Violet dot-line).